(FORTUNE Magazine) – Dear Oddsist: As a lifelong devotee of the weird, outre, and paranormal, I was naturally all aquiver on August 1 when the Dow Jones industrials rose by 33.67, a figure that "eerily matched" the gains of the previous trading day (to quote the awestruck "Abreast of the Market" commentator in the Wall Street Journal). It hardly seems possible that chance alone could produce so precise a matchup, and I was wondering if you might conceivably descry significance in the fact that it happened soon after those comets started banging into my favorite planet, Jupiter. Dear Weirdo: The phenomenon in question seems less eerie than your persona and the odds against such double-headers are less long than you think. In confronting data like the Dow Jones averages and daily price changes, both of which are carried out to two decimal places, one normally assumes that 100 different results are possible on the right side of the decimal point. That is not the case here. Considerably reducing the odds against a perfect matchup is the fact that, for any given figure on the left side of the decimal point, only three or (rarely) four results are possible on the right side. One can hear even nonweirdos saying "huh?" but bear with us. In calculating the daily changes in its industrial average, Dow Jones adds up the price changes in the 30 underlying stocks and divides the total by its famous divisor, which these days is 0.38610730. (It changes anytime a Dow stock splits.) On both of the trading days you cite, the sum of the 30 stocks'gains and losses came to exactly 13. Dividing that figure by the divisor is what gave the Dow its gain of 33.67. If the sum had been 131/8, which is the next- highest possibility, then the Dow would have been up by 33.99. The divisor ensures that each 1/8 point added to stock prices adds .32 to the average. How improbable is a Dow day that perfectly matches the previous day? On the overwhelming majority of days, the industrials close up or down by 50 points or less -- i.e., there are 101 possibilities for the left side of the decimal point. For the right side, there are on average 3.089 possibilities (because .32 goes into 1.00 some 3.089 times). Multiplying that figure by 101, we get 312 possible price changes. Let us assume for the moment that all of them are equally probable. In that case, we can say that on any given day the likelihood of yesterday's price change being repeated is 1/312, and of its not being repeated is 311/312, or .9968. But that's just one day. The New York Stock Exchange in a typical year is open 253 days, so the likelihood of no repetitions during the course of a year is .9968 multiplied by itself 253 times, which works out to .444. Hmm. That figure means that there is a 55.6% probability of at least one repetition during a year. Actually, this calculation somewhat understates the likelihood of price repetitions, since it assumes that any change between +50 and 50 points is as probable as any other. In reality, smaller changes are more common. Mr. Statistics has created a computer simulation of the market in which each of the 30 industrial stocks is allowed to fluctuate randomly between +2.5 and ---2.5 on any one day, but higher probabilities are assigned to smaller fluctuations. Using this simulation to generate Dow price changes over 1,000 market days, he found six repetitions -- despite an eerie dry spell of 721 consecutive days with none.

Dear Morningliner: As a lobbyist and hobbyist, I spend a lot of time reading the Washington Post and trying to estimate the IQs of the governing classes (that's my hobby), and recently I came across some most illuminating data. The Post solemnly reported on August 1 that numerous capital big shots, including dozens of congressional staff members, are playing a new pyramid game called Airplane. It said that a principal promoter of the game is a former U.S. Treasury official but did not indicate which Administration he worked for. Finally, it noted that "ethical specialists" -- as you know, we have a lot of those here -- fear the game could result in players becoming "inappropriately beholden to one another." Please tell me the odds of winning at Airplane, as this info could affect quite a few of my moron ratings. Dear Lobhob: In the game you describe, the players are a so-called pilot, two copilots, four crew members, and eight passengers. To play, you put up $1,000 and become a passenger. As soon as there are eight passengers, the pilot collects $8,000 and departs with his $7,000 profit. At this point, the airplane becomes two planes, with each of the copilots moving up to pilot and everybody else also moving up a rank. This means that 16 passengers must be found to replace the original eight. In our nation's capital, where numerous folks are ever eager to become inappropriately beholden to one another, this doubling process could go on for quite a while. What might be the limit? Plucking a figure out of the ozone, one posits that even with repeaters, it is hard to imagine more than 15,000 Washingtonians being sufficiently rich, dumb, or corrupt enough to play the game. This would mean that the odds favor an airplane crash somewhere around the 11th generation (because 2 to the 11th power times 8 equals 16,384). It may have already crashed as you read these lines, in which case Geoffrey Peterson, a Deputy Assistant Secretary of the Treasury in the Carter Administration (his area of responsibility was tax legislation), needs something else to promote.